def test_msolve():
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T)
# numeric.newton is tested in this example too
for x0 in [(-1., 1.), (1., -2.), (4., 4.), (-4., -4.)]:
x = msolve((x1, x2), f, x0, tol=1.e-8)
assert maxnorm(F(*x)) <= 1.e-11
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2*y
f2 = (x**2 + x*(y**2 - 2) - 4*y) / (x + 4)
f3 = sqrt(x**2 + y**2)*z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T)
def getroot(x0):
root = msolve((x, y, z), (f1, f2, f3), x0)
assert maxnorm(F(*root)) <= 1.e-8
return root
assert map(round, getroot((1., 1., 1.))) == [2.0, 1.0, 0.0]
def test_msolve():
x1 = Symbol('x1')
x2 = Symbol('x2')
f1 = 3 * x1**2 - 2 * x2**2 - 1
f2 = x1**2 - 2 * x1 + x2**2 + 2 * x2 - 8
f = Matrix((f1, f2)).T
F = lambdify((x1, x2), f.T)
# numeric.newton is tested in this example too
for x0 in [(-1., 1.), (1., -2.), (4., 4.), (-4., -4.)]:
x = msolve((x1, x2), f, x0, tol=1.e-8)
assert maxnorm(F(*x)) <= 1.e-11
# The Chinese mathematician Zhu Shijie was the very first to solve this
# nonlinear system 700 years ago (z was added to make it 3-dimensional)
x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
f1 = -x + 2 * y
f2 = (x**2 + x * (y**2 - 2) - 4 * y) / (x + 4)
f3 = sqrt(x**2 + y**2) * z
f = Matrix((f1, f2, f3)).T
F = lambdify((x, y, z), f.T)
def getroot(x0):
root = msolve((x, y, z), (f1, f2, f3), x0)
assert maxnorm(F(*root)) <= 1.e-8
return root
assert map(round, getroot((1., 1., 1.))) == [2.0, 1.0, 0.0]
def getroot(x0):
root = msolve((x, y, z), (f1, f2, f3), x0)
assert maxnorm(F(*root)) <= 1.e-8
return root
def getroot(x0):
root = msolve((x, y, z), (f1, f2, f3), x0)
assert maxnorm(F(*root)) <= 1.e-8
return root